Members of election committee empty a ballot box after voting closed at a polling station in Donetsk, Ukraine, Sunday, May 11, 2014. (AP/Evgeniy Maloletka)

KYIV, Ukraine — Before Petro Poroshenko, who won Ukraine’s presidency in the election on Sunday, had even detailed his priorities in a post-election press conference Monday, he was slapped with a fresh raft of reminders of just how tough his job will be.

By dawn, armed pro-Russian rebels had seized the central airport in Donetsk, the regional capital of the industrialized eastern heartland and the hotbed of Ukraine’s separatist movement. Flights were suspended , and clashes with pro-government forces erupted shortly after.

Meanwhile, the leader of the self-declared “People’s Republic of Donetsk” dismissed the election results and declared a “military situation” in the region, Russian news agencies reported.

With people still shooting and the country more divided — physically, mentally and otherwise — than ever, experts say Poroshenko, who has vowed to repair relations with Russia while reining in the separatists, faces a tougher battle than any of his predecessors.

“He needs to create a new state practically from scratch,” said Vadim Karasyov, director of Kyiv-based think tank Institute of Global Strategies.

International election observers praised Sunday’s vote — which appeared to draw about 60 percent of the electorate — as generally in accordance with international standards.

With more than 85 percent of the ballots counted by Monday evening, Poroshenko had secured 54 percent of the vote versus former Prime Minister Yulia Tymoshenko’s 13 percent.

But his victory was somewhat hampered by a coordinated effort on the part of pro-Russian separatists in the east to disrupt the vote there through intimidation and threats of violence.

According to preliminary findings by the Organization for Security and Cooperation in Europe (OSCE), voting did not take place in 10 out of the 12 electoral districts in the Luhansk Region and 14 of 22 in the Donetsk Region.

On Monday, Poroshenko promised to seek dialogue with any anti-Kyiv activists who lay down their arms, but refused to negotiate with “terrorists” who he claims threaten national security.

Poroshenko also pledged to keep up the military’s “anti-terrorist” operation that’s largely floundered in recent weeks, but promised to boost its efficiency.

Some experts argue that how he handles the uprising in the east may directly affect the chances for dialogue with Moscow, which has maintained that months-long protests in the Ukrainian capital against Russian-aligned former president Viktor Yanukovych were a fascist-led “coup” engineered by the West.

While Moscow has since distanced itself from Ukraine’s pro-Russian rebel leadership, it has nevertheless urged Kyiv to reach out to the separatists, which the Kremlin sees as peaceful protesters.

“Poroshenko is likely to give separatists a deadline to lay down arms or to face the consequences of a military campaign against them –– let’s see how Moscow reacts to this, if there are then large-scale casualties on the ground,” Timothy Ash, an analyst at Standard Bank in London, wrote in an op-ed published Monday in the Kyiv Post.

Russian President Vladimir Putin had signaled even before the vote that he looked forward to working with Ukraine’s newly elected president.

Other top officials — such as Foreign Minister Sergei Lavrov — repeated that sentiment on Monday.

“Taking into account the expression of will that has taken place, which we respect, we will be prepared to establish pragmatic, equitable dialogue on the existing foundation,” Reuters reported Lavrov as saying.

But he added that Kyiv’s resumption of its military campaign in the east would be a “colossal mistake.”

It remains to be seen just how much the Kremlin’s willing to back up its words, especially after Monday’s rebel airport raid was answered by a fierce Ukrainian military assault.

Media reports from the scene detailed a steady exchange of automatic weapons fire while Ukrainian fighter jets reportedly launched airstrikes on the area.

But as if the simmering violence wasn’t enough, Poroshenko also faces the challenge of consolidating political support for his policies.

While he’s enjoyed widespread popular approval thanks to his business acumen and visible role during the protest movement, he’ll operate under a new constitution that weakens the presidency and strengthens the parliament.

Poroshenko nominally leads his own political party, but it’s little more than a legal entity and has no influence of its own.

That’s partially why he teamed up with world champion boxer-cum-politician Vitali Klitschko — who won Sunday’s simultaneous Kyiv mayoral elections — earlier this spring in a high-profile political union.

Klitschko’s party, the Ukrainian Democratic Alliance for Reform (UDAR), is already the third largest in parliament and might be of use for Poroshenko.

Or, observers say, the president-elect might seek to create his own political vehicle to burnish his support.

Either way, says Serhiy Leshchenko, a prominent Ukrainian journalist, Poroshenko’s main political goal will be to dismiss parliament and call snap elections — which Poroshenko has already said he’ll do — as early as possible.

That would amount to capitalizing on his current approval ratings before it’s too late, especially in the mercurial world of Ukrainian politics.

“Because I don’t think he’ll ever have such a high level of support again,” Leshchenko said.

Other experts agree, adding that Poroshenko will have to tread carefully.